Teaching at the Chennai campus of Vellore Institute of
Technology, exclusively to engineering students since 2011.
In an earlier job was teaching Mathematics majors; missing that atmosphere drove me to search for this type of site.

Primes as uncorrelated random variablesI once saw a heuristic argument that the probability of two numbers being relatively prime is $6/\pi^2$, the computation involving calculating the value of Euler's zeta function value $\zeta(2)$. How does this gel with this?

How to handle a polynomial whose roots exhibit obvious symmetryYou say you expect to reduce the polynomial because of cyclic group of order 3. What exactly do you mean by reducing? Your polynomials are not irreducible? And your plot needs info on how to interpret: are the dots hights represent roots (real numbers always?) Multiple dots at same level does that means roots of same modulus?

Is there any Lefschetz-like principle for representations of finite groups?Nice to get a comment from the master himself! Thanks for your explicit statement about divisibility that I did not know earlier. (Perhaps I did not study the textbooks carefully). As the divisibility proofs used the fact an algebraic integer that is rational is a usual integer I could not guess about representations in prime characteristic.